Existing human-robot interaction (HRI) technologies are not intuitive or effective enough for the disabled. Most of them can neither express their explicit intent (voice, posture, touch, etc.), nor communicate based on implicit intent. We propose a novel HRI framework for implicit intent reasoning based on eye tracking. The framework is designed for people with normal vision, and it will track and analyze their eye movements to infer their intents in a smart home environment. These intents are then sent to an assistive robot and guide the robot to accomplish specific tasks such as using keys to open the door. Two Experiments were carried out to validate the effectiveness of the framework. In the implicit intents classification task, the average classification accuracy of the two implicit intents (task-free visual browsing and task-oriented visual search) was 84.43% via the Support Vector Machine (SVM). In implicit intent reasoning task, Naive Bayesian (NB) networks were used to establish the intent knowledge base, reaching the highest accuracy of intent reasoning was 98%. These results proved that our framework could aid the elderly and the disabled to better adapt to the smart home environment in their daily life.